a) 423 cm = 4,23 m

b) 806 cm = 8,06 m

c) 24 dm = 2,4 m

d) 75 cm = 7,5 dm

a) \(\dfrac{4}{15}< \dfrac{3}{5}\)

Vì khi quy đồng \(\dfrac{3}{5}=\dfrac{3x3}{5x3}=\dfrac{9}{15}\)

Vì \(\dfrac{4}{15}< \dfrac{9}{15}\) nên \(\dfrac{4}{15}< \dfrac{3}{5}\)

b) \(\dfrac{2}{3}>\dfrac{4}{7}\)

Vì khi quy đồng \(\dfrac{2}{3}=\dfrac{2x7}{3x7}=\dfrac{14}{21}\); \(\dfrac{4}{7}=\dfrac{4x3}{7x3}=\dfrac{12}{21}\) nên \(\dfrac{2}{3}>\dfrac{4}{7}\)

c) \(\dfrac{15}{12}>\dfrac{20}{28}\)

Vì khi quy đồng \(\dfrac{15}{12}=\dfrac{15x28}{12x28}=\dfrac{420}{336}\) ; \(\dfrac{20}{28}=\dfrac{20x12}{28x12}=\dfrac{240}{336}\) nên \(\dfrac{15}{12}>\dfrac{20}{28}\)

A = \(-\dfrac{3}{17}+\left(\dfrac{2}{3}+\dfrac{3}{17}\right)\)

A = \(-\dfrac{3}{17}+\dfrac{43}{51}\)

A = \(\dfrac{2}{3}\)

B = \(-\dfrac{5}{7}+\dfrac{3}{4}+\dfrac{1}{5}+-\dfrac{2}{7}+\dfrac{1}{4}\)

B = \(-\dfrac{5}{7}+\dfrac{3}{4}+\dfrac{1}{5}-\dfrac{2}{7}+\dfrac{1}{4}\)

B = \(\dfrac{1}{5}\)

C = \(\left(-\dfrac{9}{25}\right)\) x \(\dfrac{53}{3}-\left(-\dfrac{3}{5}\right)2\) x \(\dfrac{2}{3}2\)

C = \(-\dfrac{9}{25}\) x \(\dfrac{53}{3}-\left(-\dfrac{3}{5}\right)^2\left(\dfrac{2}{3}\right)^2\)

C = \(-\dfrac{159}{25}-\left(-\dfrac{3}{5}\right)^2\left(\dfrac{2}{3}\right)^2\)

C = \(-\dfrac{159}{25}-\left(\dfrac{3}{5}\right)^2\left(\dfrac{2}{3}\right)^2\)

C = \(\dfrac{159}{25}-\dfrac{3^2}{5^2}\left(\dfrac{2}{3}\right)^2\)

C = \(-\dfrac{159}{25}-\dfrac{9}{25}\left(\dfrac{2}{3}\right)^2\)

C = \(-\dfrac{159}{25}-\dfrac{9}{25}\) x \(\dfrac{2^2}{3^2}\)

C = \(-\dfrac{159}{25}-\dfrac{9}{25}\) x \(\dfrac{4}{9}\)

C = \(-\dfrac{159}{25}-\dfrac{4}{25}\)

C = \(-\dfrac{163}{25}\)

a) 2011 + 2011 + 2011 + 2011 - 2008 x 4

= 2011 + 2011 + 2011 + 2011 - 8032

= 12

b) 72 x 55 + 216 x 15

= 3960 + 216 x 15

= 3960 + 3240

= 7200

c) 250 x 755 - 161 x 37 + 253 x 25 - 161 x \(\dfrac{63}{100}\) x 47 - 12 x 3,5 - 5,8 : 0,1

= \(\dfrac{18425079}{100}\)

a) \(x+\dfrac{3}{4}=\dfrac{11}{6}-\dfrac{3}{24}:\dfrac{15}{4}\)

    \(x+\dfrac{3}{4}=\dfrac{11}{6}-\dfrac{1}{30}\)

    \(x+\dfrac{3}{4}=\dfrac{9}{5}\)

    \(x=\dfrac{9}{5}-\dfrac{3}{4}\)

    \(x=\dfrac{21}{20}\)

b) \(x-\dfrac{3}{7}+\dfrac{1}{2}:\dfrac{3}{4}=\dfrac{13}{14}\)

    \(x-\dfrac{3}{7}+\dfrac{2}{3}=\dfrac{13}{14}\)

    \(x+\dfrac{5}{21}=\dfrac{13}{14}\)

    \(x=\dfrac{13}{14}-\dfrac{5}{21}\)

    \(x=\dfrac{29}{42}\)

a) \(x+\dfrac{3}{4}=\dfrac{11}{6}-\dfrac{3}{24}:\dfrac{15}{24}\)

    \(x+\dfrac{3}{4}=\dfrac{11}{6}-\dfrac{1}{5}\)

    \(x+\dfrac{3}{4}=\dfrac{49}{30}\)

    \(x=\dfrac{49}{30}-\dfrac{3}{4}\)

   \(x=\dfrac{53}{60}\) 

b) \(x-\dfrac{3}{7}+\dfrac{1}{2}:\dfrac{3}{4}=\dfrac{13}{14}\)  

    \(x-\dfrac{3}{7}+\dfrac{2}{3}=\dfrac{13}{14}\)

    \(x+\dfrac{5}{21}=\dfrac{13}{14}\)

    \(x=\dfrac{13}{14}-\dfrac{5}{21}\)

    \(x=\dfrac{29}{42}\)

   322,18 : 8,9 

\(=\dfrac{16109}{50}:8,9\)

\(=\dfrac{16109}{50}:\dfrac{89}{10}\)

\(=\dfrac{16109}{50}\) x \(\dfrac{10}{89}\)

\(=\dfrac{181}{5}\)

so sánh \(\dfrac{2}{3}< \dfrac{3}{4}\)

Trung bình cộng là :

( 2 + 200 ) : 2 = 101

          Đáp số : 101

*) Từ 1 đến 9 có 5 số

*) Từ 11 đến 99 có ( 99 - 11 ) : 2 + 1 = 45 ( số )

⇒ Có : 45 x 2 = 90 ( chữ số )

*) Từ 101 đến 999 có ( 999 - 101 ) : 2 + 1 = 450 ( số )

⇒ Có  : 450 x 3 = 1350 ( chữ số )

*) Từ 1001 đến 2005 có ( 2005 - 1001 ) : 2 + 1 = 503 ( số )

⇒ Có : 503 x 4 = 2012 ( chữ số )

Vậy Duy đã dùng tất cả :

5 + 90 + 1350 + 2012 = 3457 ( chữ số )